incrementing LATEX fraction recursively in C

i am trying to write a program that gets input step and prints the following in LATEX format .(https://i.sstatic.net/cF4Kc9gY.png)](https://i.sstatic.net/cF4Kc9gY.png)
for example for step = 3 , the output is 1+\frac{2+\frac{4}{5}}{3+\frac{6}{7}}

this is the code i have write now but i get *** stack smashing detected ***: terminated error for inputs more than 6. any idea how to manage this ? (at least for inputs lower than 10)

#include <stdio.h>
#include <stdlib.h>

void frac(int start, int step, char *result) {
    if (step == 1) {
        sprintf(result, "%d", start);
    } else {
        char left[256];
        char right[256];
        frac(2 * start, step - 1, left);
        frac(2 * start + 1, step - 1, right);
        sprintf(result, "%d+\\frac{%s}{%s}", start, left, right);
    }
}

int main() {
    int step;
    scanf("%d", &step);
    
    char result[1024];
    int start = 1;
    frac(start, step, result);
    printf("%s\n", result);
    
    return 0;
}

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